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A 20v battery with internal resistance of 5 ohms is connected to a resistor of x Ohms. If an additional 6ohms resistor is connected across the battery, find the value of x so that the external power supplied by the battery remains the same.?
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A 20v battery with internal resistance of 5 ohms is connected to a res...
Introduction:
In this problem, we are given a 20V battery with internal resistance of 5 ohms and we need to find the value of x Ohms for the external resistor so that the external power supplied by the battery remains the same even after an additional 6 ohms resistor is connected across the battery.
Solution:
We know that the power supplied by the battery is given by:
P = V^2/(R + r)
where V is the voltage of the battery, R is the external resistance, and r is the internal resistance.
Now, when the additional 6 ohms resistor is connected across the battery, the total external resistance becomes (R + 6).
The power supplied by the battery after the resistor is connected is given by:
P' = V^2 / (R + 6 + r)
We are given that the external power supplied by the battery remains the same, i.e. P = P', so we can equate the two equations:
V^2/(R + r) = V^2/(R + 6 + r)
Simplifying the equation, we get:
R + r = R + 6 + r
R = 6 ohms
Therefore, the value of x Ohms for the external resistor is 6 ohms.
Conclusion:
In this problem, we found the value of x Ohms for the external resistor so that the external power supplied by the battery remains the same even after an additional 6 ohms resistor is connected across the battery. We used the formula for power supplied by the battery and equated it before and after the additional resistor was connected to get the value of x.
In this problem, we are given a 20V battery with internal resistance of 5 ohms and we need to find the value of x Ohms for the external resistor so that the external power supplied by the battery remains the same even after an additional 6 ohms resistor is connected across the battery.
Solution:
We know that the power supplied by the battery is given by:
P = V^2/(R + r)
where V is the voltage of the battery, R is the external resistance, and r is the internal resistance.
Now, when the additional 6 ohms resistor is connected across the battery, the total external resistance becomes (R + 6).
The power supplied by the battery after the resistor is connected is given by:
P' = V^2 / (R + 6 + r)
We are given that the external power supplied by the battery remains the same, i.e. P = P', so we can equate the two equations:
V^2/(R + r) = V^2/(R + 6 + r)
Simplifying the equation, we get:
R + r = R + 6 + r
R = 6 ohms
Therefore, the value of x Ohms for the external resistor is 6 ohms.
Conclusion:
In this problem, we found the value of x Ohms for the external resistor so that the external power supplied by the battery remains the same even after an additional 6 ohms resistor is connected across the battery. We used the formula for power supplied by the battery and equated it before and after the additional resistor was connected to get the value of x.
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A 20v battery with internal resistance of 5 ohms is connected to a resistor of x Ohms. If an additional 6ohms resistor is connected across the battery, find the value of x so that the external power supplied by the battery remains the same.?
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A 20v battery with internal resistance of 5 ohms is connected to a resistor of x Ohms. If an additional 6ohms resistor is connected across the battery, find the value of x so that the external power supplied by the battery remains the same.? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A 20v battery with internal resistance of 5 ohms is connected to a resistor of x Ohms. If an additional 6ohms resistor is connected across the battery, find the value of x so that the external power supplied by the battery remains the same.? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 20v battery with internal resistance of 5 ohms is connected to a resistor of x Ohms. If an additional 6ohms resistor is connected across the battery, find the value of x so that the external power supplied by the battery remains the same.?.
A 20v battery with internal resistance of 5 ohms is connected to a resistor of x Ohms. If an additional 6ohms resistor is connected across the battery, find the value of x so that the external power supplied by the battery remains the same.? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A 20v battery with internal resistance of 5 ohms is connected to a resistor of x Ohms. If an additional 6ohms resistor is connected across the battery, find the value of x so that the external power supplied by the battery remains the same.? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 20v battery with internal resistance of 5 ohms is connected to a resistor of x Ohms. If an additional 6ohms resistor is connected across the battery, find the value of x so that the external power supplied by the battery remains the same.?.
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